Originally posted by StephenPrivitera How is eccentricity of an orbit affected by the angular momentum of the orbiting body (mathematically, that is)? How does torque affect angular momentum? How is a torque exerted? What is a torque?

All of the following is at the level of Newton-Kepler orbits.

Angular momentum does not affect the eccentricity, or vice versa. The eccentricity does not change greatly, unless there are tidal effects. Angular momentum is conserved. They interact to cause the planet's speed to vary according to Kepler's second law: A radius vector from the planet to the sun sweeps out equal areas in equal times.

Torque is twisting force, given by a force acting on a lever arm, or equivalent. You can use torque to develop Keplerian orbits, and there used to be a web site that did this, but I have lost the link.